SOLUTION: A paddleboat can move at a speed of 20 km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the

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Question 1000200: A paddleboat can move at a speed of 20 km/h in still water. The boat is paddled 6 km downstream in a river in the same time it takes to go 3 km upstream. What is the speed of the river?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +r+ = the speed of the river in km/hr
+20+%2B+r+ = the speed of the paddleboat going downstream in km/hr
+20+-+r+ = th speed of the paddleboat going upstream in km/hr
Let +t+ = time in hrs to go upstream or downstream
----------------------------
Going downstream:
(1) +6+=+%28+20+%2B+r+%29%2At+
Going upstream:
(2) +3+=+%28+20+-+r+%29%2At+
--------------------
(1) +t+=+6%2F%28+20%2Br+%29+
and
(2) +t+=+3%2F%28+20-r+%29+
--------------------
+6%2F%28+20%2Br+%29+=+3%2F%28+20-r+%29+
+6%2A%28+20-r+%29+=+3%2A%28+20%2Br+%29+
+120+-+6r+=+60+%2B+3r+
+9r+=+60+
+r+=+20%2F3+
+r+=+6.667+ km/hr
-------------------
check answer:
(1) +t+=+6%2F%28+20%2Br+%29+
(1) +t+=+6%2F%28+20%2B6.667+%29+
(1) +t+=+6%2F26.667+
and
(2) +t+=+3%2F%28+20-r+%29+
(2) +t+=+3%2F%28+20-6.667+%29+
(2) +t+=+3%2F13.333+
(2) +t+=+6%2F26.667+
OK